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S hape Matching and Classification Using Height FunctionsPowerPoint Presentation

S hape Matching and Classification Using Height Functions

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### Shape Matching and Classification Using Height Functions

Xide Xia

ENGN 2560

Advisor: Prof. Kimia

Project Initial Presentation

Shape Matching:

object recognition, character recognition, medical image and protein analysis …

- Geometric Transformations (translation, rotation, scaling, etc.)
- Nonlinear Deformations (noise, articulation and occlusion)

Steps:

- 1) Shape descriptor with height functions
- 2) Similarity measure using the height descriptor

Shape descriptor with height functions:

- A sequence of equidistant sample points X:
X={Xi} , i=1,2,….,N

- Tangent line Li:
its direction is always starting from Xi-1 to Xi+1

- Height value Hi:
the symboled distance between the jth (j = 1,. . . ,N) sample point Xj and the tangent line Li is defined as a height value hi,j.

(the height value of the jth sample point Xj according to the reference axis Li of the point Xi)

Descriptor Hi the reference axis Li of the point Xi)：

- the direction of the reference axis Li
- the location of the sample point Xi on the shape contour X.

- Smoothed height values: the reference axis Li of the point Xi)

F is an M *N matrix with column i being the shape descriptor Fi of the sample point Xi.

- Local nomalization: the reference axis Li of the point Xi)

Consequently, the value of each entry in the matrix F after normalization is in the interval [-1, 1].

Similarity measure using the height descriptor: the reference axis Li of the point Xi)

In shape recognition, we usually compute a shape similarity or dissimilarity (distance) to find the optimal correspondence of contour points.

Dynamic Programming (DP) algorithm to find the correspondence

The shape dissimilarity: the sum of the distances of the corresponding points.

- The cost (distance) of matching p and q: the reference axis Li of the point Xi)
- Weight coefficient
- Dissimilarity between the two shapes:

Given two shapes X and Y. With DP we compute an optimal correspondence x to y that the is minimal.

Humans are generally more sensitive to contour deformations when the complexity of the contour is lower!

- Shape complexity:

where std denotes the standard deviation.

- The dissimilarity or distance between two shapes X, Y normalized by their shape complexity values:

where the factor is used to avoid divide-by-zero.

Shape descriptor with height functions: normalized by their shape complexity values:

- A sequence of equidistant sample points X
- Tangent line Li
- Height value Hi
- Smoothed height values
- Local nomalization

Similarity measure using the height descriptor:

- The cost (distance) of matching p and q
- Weight coefficient
- Dissimilarity between the two shapes
- Shape complexity
- Dissimilarity normalized by complexity values

Schedule: normalized by their shape complexity values:

- 1st week: Learn the algorithm well
- 2nd ~3th week: Write up the codes of the shape descriptor part
- 4th ~5th week: Write up the codes of the matching part
- 6th~7th week: Debug and Test in different datasets, Make Comparison with other shape matching algorithm (Shock Graphs)
- 8th week: Make conclusion, Prepare for the final presentation

Thank you normalized by their shape complexity values:

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